On the limited memory BFGS method for large scale optimization
Mathematical Programming: Series A and B
High-order accurate discontinuous finite element solution of the 2D Euler equations
Journal of Computational Physics
A comparison of two optimization methods for mesh quality improvement
Engineering with Computers
Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications
Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications
Journal of Computational Physics
Adaptive mesh generation for curved domains
Applied Numerical Mathematics - Adaptive methods for partial differential equations and large-scale computation
A content-aware bridging service for publish/subscribe environments
Journal of Systems and Software
The generation of arbitrary order curved meshes for 3D finite element analysis
Computational Mechanics
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This paper presents a technique that allows to untangle high-order/curvilinear meshes. The technique makes use of unconstrained optimization where element Jacobians are constrained to lie in a prescribed range through moving log-barriers. The untangling procedure starts from a possibly invalid curvilinear mesh and moves mesh vertices with the objective of producing elements that all have bounded Jacobians. Bounds on Jacobians are computed using the results of Johnen et al. (2012, 2013) [1,2]. The technique is applicable to any kind of polynomial element, for surface, volume, hybrid or boundary layer meshes. A series of examples demonstrate both the robustness and the efficiency of the technique. The final example, involving a time explicit computation, shows that it is possible to control the stable time step of the computation for curvilinear meshes through an alternative element deformation measure.